1) Estimate a simple linear regression model predicting Oil Usage from Degree Da

Question

1) Estimate a simple linear regression model predicting Oil Usage from Degree Days. Is this model statistically significant?

No

Yes

QUESTION 2

[2] How much of the variation in Oil Usage is explained by the variation in Degree Days?

54.3%

29.4%

150.36%

0.29%

  

QUESTION 3

[3] Based on the simple regression model, for each one unit increase in Degree Days, Oil Usage increases by __________ units.

3.98

58.80

0.25

29.4%

QUESTION 4

[4] The Y-intercept of the simple regression model predicting Oil Usage from Degree Days is significantly different from 0 in the population.

Yes

NO

QUESTION 5

[5] Predict Oil Usage for all 40 customers using all remaining varaibles as predictors. This regression model predicts _______ more variation in Oil Usage than that predicted by the simple regression model.

34%

49%

0.49%

65%

QUESTION 6

[6] Each individual predictor in the multiple regression model has a significant effect on Oil Usage.

True

False

  

QUESTION 7

[7] The Y-intercept of the multiple regression model is significantly different from 0 in the population.

Yes

No

QUESTION 8

[8] The predicted Oil Usage of a customer for whom Degree Days equal 600, Home Index value is 3, and number of people living in the house is 4, is approximately:

665

229

180

365

QUESTION 9

[9] The predicted Oil Usage of a customer for whom Degree Days equal 458, Home Index value is 1, and number of people living in the house is 1, is approximately:

1

0

242

-7

QUESTION 10

[10] The multiple regression model suggests that about 78% of the variation in the predictors can be explained by Oil Usage.

False

True

Customer Oil Usage Degree Days Home Index Number People 1 381 888 3 3 2 171 176 5 7 3 644 1073 5 4 4 19 126 2 4 5 394 645 5 5 6 153 326 4 6 7 7 1229 1 3 8 319 1218 2 4 9 40 570 2 1 10 121 334 1 7 11 243 738 3 3 12 200 1464 1 5 13 402 880 4 5 14 118 1134 1 5 15 319 1019 3 4 16 185 460 2 3 17 209 257 5 4 18 467 779 5 4 19 50 128 2 4 20 153 371 2 5 21 94 178 3 6 22 574 933 5 3 23 191 295 3 5 24 679 1358 4 5 25 305 626 4 5 26 85 237 2 7 27 87 813 1 6 28 170 385 3 5 29 92 678 1 4 30 35 54 2 3 31 60 314 1 5 32 507 898 4 3 33 148 966 1 6 34 83 84 5 3 35 318 919 3 4 36 85 379 1 4 37 245 512 3 4 38 56 355 2 3 39 303 759 3 3 40 10 777 1 4

Explanation / Answer

below is regrssion output with degree days:

1)Yes ; as p value is very low

2) variation in Oil Usage is explained by the variation in Degree Days =R2 =29.4%

3) Oil Usage increases by =0.25

4)

NO as p value is very high

5)

with all variable ; below is regression output:

difference in R2 =49.9%

6)

false ; as p value for number people is very high

7)Yes

8)229

9)0

10)

true

Regression Statistics Multiple R 0.5427 R Square 0.2945 Adjusted R Square 0.2759 Standard Error 150.3603 Observations 40.0000 ANOVA df SS MS F Significance F Regression 1.0000 358595.0620 358595.0620 15.8613 0.0003 Residual 38.0000 859112.8380 22608.2326 Total 39.0000 1217707.9000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 58.8035 46.5192 1.2641 0.2139 -35.3696 152.9767 Degree Days 0.2514 0.0631 3.9826 0.0003 0.1236 0.3792

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